{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Sebastian Raschka](http://sebastianraschka.com)  \n",
    "<br>\n",
    "[Link to](https://github.com/rasbt/pattern_classification) the GitHub repository [pattern_classification](https://github.com/rasbt/pattern_classification)\n",
    "<br><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "Last updated: 07/30/2015 \n",
      "\n",
      "CPython 3.4.3\n",
      "IPython 3.2.1\n",
      "\n",
      "scikit-learn 0.16.1\n",
      "numpy 1.9.2\n",
      "matplotlib 1.4.3\n"
     ]
    }
   ],
   "source": [
    "%watermark -a 'Sebastian Raschka' -d -u -v -p scikit-learn,numpy,matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "I would be happy to hear your comments and suggestions.  \n",
    "Please feel free to drop me a note via\n",
    "[twitter](https://twitter.com/rasbt), [email](mailto:bluewoodtree@gmail.com), or [google+](https://plus.google.com/+SebastianRaschka).\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# About Feature Scaling: Z-Score Standardization and Min-Max Scaling "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [About standardization](#About-standardization)\n",
    "- [About Min-Max scaling / \"normalization\"](#About-Min-Max-scaling-normalization)\n",
    "- [Standardization or Min-Max scaling?](#Standardization-or-Min-Max-scaling?)\n",
    "- [Standardizing and normalizing - how it can be done using scikit-learn](#Standardizing-and-normalizing---how-it-can-be-done-using-scikit-learn)\n",
    "- [Bottom-up approaches](#Bottom-up-approaches)\n",
    "- [The effect of standardization on PCA in a pattern classification task](#The-effect-of-standardization-on-PCA-in-a-pattern-classification-task)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## About standardization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of **standardization** (or **Z-score normalization**) is that the features will be rescaled so that they'll have the properties of a standard normal distribution with   \n",
    "\n",
    "$\\mu = 0$ and $\\sigma = 1$\n",
    "\n",
    "where $\\mu$ is the mean (average) and $\\sigma$ is the standard deviation from the mean; standard scores (also called ***z*** scores) of the samples are calculated as follows:\n",
    "\n",
    "\\begin{equation} z = \\frac{x - \\mu}{\\sigma}\\end{equation} \n",
    "\n",
    "Standardizing the features so that they are centered around 0 with a standard deviation of 1 is not only important if we are comparing measurements that have different units, but it is also a general requirement for many machine learning algorithms. Intuitively, we can think of gradient descent as a prominent example\n",
    "(an optimization algorithm often used in logistic regression, SVMs, perceptrons, neural networks etc.); with features being on different scales, certain weights may update faster than others since the feature values $x_j$ play a role in the weight updates\n",
    "\n",
    "$$\\Delta w_j = - \\eta \\frac{\\partial J}{\\partial w_j} = \\eta \\sum_i (t^{(i)} - o^{(i)})x^{(i)}_{j},$$\n",
    "\n",
    "so that \n",
    "\n",
    "$$w_j := w_j + \\Delta w_j,$$\n",
    "where $\\eta$ is the learning rate, $t$ the target class label, and $o$ the actual output.\n",
    "Other intuitive examples include K-Nearest Neighbor algorithms and clustering algorithms that use, for example, Euclidean distance measures -- in fact, tree-based classifier are probably the only classifiers where feature scaling doesn't make a difference.\n",
    "\n",
    "\n",
    "\n",
    "To quote from the [`scikit-learn`](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html) documentation:\n",
    "\n",
    "*\"Standardization of a dataset is a common requirement for many machine learning estimators: they might behave badly if the individual feature do not more or less look like standard normally distributed data (e.g. Gaussian with 0 mean and unit variance).\"*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='About-Min-Max-scaling-normalization'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## About Min-Max scaling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An alternative approach to Z-score normalization (or standardization) is the so-called **Min-Max scaling** (often also simply called \"normalization\" - a common cause for ambiguities).  \n",
    "In this approach, the data is scaled to a fixed range - usually 0 to 1.  \n",
    "The cost of having this bounded range - in contrast to standardization - is that we will end up with smaller standard deviations, which can suppress the effect of outliers.\n",
    "\n",
    "A Min-Max scaling is typically done via the following equation:\n",
    "\n",
    "\\begin{equation} X_{norm} = \\frac{X - X_{min}}{X_{max}-X_{min}} \\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Z-score standardization or Min-Max scaling?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*\"Standardization or Min-Max scaling?\"* - There is no obvious answer to this question: it really depends on the application. \n",
    "\n",
    "For example, in clustering analyses, standardization may be especially crucial in order to compare similarities between features based on certain distance measures. Another prominent example is the Principal Component Analysis, where we usually prefer standardization over Min-Max scaling, since we are interested in the components that maximize the variance (depending on the question and if the PCA computes the components via the correlation matrix instead of the covariance matrix; [but more about PCA in my previous article](http://sebastianraschka.com/Articles/2014_pca_step_by_step.html)).\n",
    "\n",
    "However, this doesn't mean that Min-Max scaling is not useful at all! A popular application is image processing, where pixel intensities have to be normalized to fit within a certain range (i.e., 0 to 255 for the RGB color range). Also, typical neural network algorithm require data that on a 0-1 scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standardizing and normalizing - how it can be done using scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we could make use of NumPy's vectorization capabilities to calculate the z-scores for standardization and to normalize the data using the equations that were mentioned in the previous sections. However, there is an even more convenient approach using the preprocessing module from one of Python's open-source machine learning library [scikit-learn](http://scikit-learn.org )."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka 12/07/2014 \n",
      "\n",
      "CPython 3.4.1\n",
      "IPython 2.1.0\n",
      "\n",
      "scikit-learn 0.15.0b1\n",
      "numpy 1.8.1\n",
      "pandas 0.14.0\n",
      "matplotlib 1.3.1\n"
     ]
    }
   ],
   "source": [
    "%watermark -a 'Sebastian Raschka' -d -p scikit-learn,numpy,pandas,matplotlib -v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=\"1.5em\">[More information](http://nbviewer.ipython.org/github/rasbt/python_reference/blob/master/ipython_magic/watermark.ipynb) about the `watermark` magic command extension.</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the following examples and discussion, we will have a look at the free \"Wine\" Dataset that is deposited on the UCI machine learning repository  \n",
    "(http://archive.ics.uci.edu/ml/datasets/Wine).\n",
    "\n",
    "<br>\n",
    "\n",
    "<font size=\"1\">\n",
    "**Reference:**  \n",
    "Forina, M. et al, PARVUS - An Extendible Package for Data\n",
    "Exploration, Classification and Correlation. Institute of Pharmaceutical\n",
    "and Food Analysis and Technologies, Via Brigata Salerno, \n",
    "16147 Genoa, Italy.\n",
    "\n",
    "Bache, K. & Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.\n",
    "\n",
    "</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Wine dataset consists of 3 different classes where each row correspond to a particular wine sample.\n",
    "\n",
    "The class labels (1, 2, 3) are listed in the first column, and the columns 2-14 correspond to 13 different attributes (features):\n",
    "\n",
    "1) Alcohol  \n",
    "2) Malic acid  \n",
    "..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading the wine dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Class label</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> 1</td>\n",
       "      <td> 14.23</td>\n",
       "      <td> 1.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> 1</td>\n",
       "      <td> 13.20</td>\n",
       "      <td> 1.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> 1</td>\n",
       "      <td> 13.16</td>\n",
       "      <td> 2.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> 1</td>\n",
       "      <td> 14.37</td>\n",
       "      <td> 1.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> 1</td>\n",
       "      <td> 13.24</td>\n",
       "      <td> 2.59</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Class label  Alcohol  Malic acid\n",
       "0            1    14.23        1.71\n",
       "1            1    13.20        1.78\n",
       "2            1    13.16        2.36\n",
       "3            1    14.37        1.95\n",
       "4            1    13.24        2.59"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "df = pd.io.parsers.read_csv(\n",
    "    'https://raw.githubusercontent.com/rasbt/pattern_classification/master/data/wine_data.csv', \n",
    "     header=None,\n",
    "     usecols=[0,1,2]\n",
    "    )\n",
    "\n",
    "df.columns=['Class label', 'Alcohol', 'Malic acid']\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see in the table above, the features **Alcohol** (percent/volumne) and **Malic acid** (g/l) are measured on different scales, so that ***Feature Scaling*** is necessary important prior to any comparison or combination of these data.  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Standardization and Min-Max scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "std_scale = preprocessing.StandardScaler().fit(df[['Alcohol', 'Malic acid']])\n",
    "df_std = std_scale.transform(df[['Alcohol', 'Malic acid']])\n",
    "\n",
    "minmax_scale = preprocessing.MinMaxScaler().fit(df[['Alcohol', 'Malic acid']])\n",
    "df_minmax = minmax_scale.transform(df[['Alcohol', 'Malic acid']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean after standardization:\n",
      "Alcohol=0.00, Malic acid=0.00\n",
      "\n",
      "Standard deviation after standardization:\n",
      "Alcohol=1.00, Malic acid=1.00\n"
     ]
    }
   ],
   "source": [
    "print('Mean after standardization:\\nAlcohol={:.2f}, Malic acid={:.2f}'\n",
    "      .format(df_std[:,0].mean(), df_std[:,1].mean()))\n",
    "print('\\nStandard deviation after standardization:\\nAlcohol={:.2f}, Malic acid={:.2f}'\n",
    "      .format(df_std[:,0].std(), df_std[:,1].std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min-value after min-max scaling:\n",
      "Alcohol=0.00, Malic acid=0.00\n",
      "\n",
      "Max-value after min-max scaling:\n",
      "Alcohol=1.00, Malic acid=1.00\n"
     ]
    }
   ],
   "source": [
    "print('Min-value after min-max scaling:\\nAlcohol={:.2f}, Malic acid={:.2f}'\n",
    "      .format(df_minmax[:,0].min(), df_minmax[:,1].min()))\n",
    "print('\\nMax-value after min-max scaling:\\nAlcohol={:.2f}, Malic acid={:.2f}'\n",
    "      .format(df_minmax[:,0].max(), df_minmax[:,1].max()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6vvnmG/bu3UunTp0IDg7mjjvuIDc3t0HpV6bKW5927NjBtGnTWLduXZUWoXvu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tLbywf7okVswmm9zqCbxwP8+teDloHjww9ZoS8rC/jgA6oMl4siqKmJCubSJX5eVgZkZqK+nlrJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1056dbe48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def plot():\n",
    "    plt.figure(figsize=(8,6))\n",
    "\n",
    "    plt.scatter(df['Alcohol'], df['Malic acid'], \n",
    "            color='green', label='input scale', alpha=0.5)\n",
    "\n",
    "    plt.scatter(df_std[:,0], df_std[:,1], color='red', \n",
    "            label='Standardized [$N  (\\mu=0, \\; \\sigma=1)$]', alpha=0.3)\n",
    "\n",
    "    plt.scatter(df_minmax[:,0], df_minmax[:,1], \n",
    "            color='blue', label='min-max scaled [min=0, max=1]', alpha=0.3)\n",
    "\n",
    "    plt.title('Alcohol and Malic Acid content of the wine dataset')\n",
    "    plt.xlabel('Alcohol')\n",
    "    plt.ylabel('Malic Acid')\n",
    "    plt.legend(loc='upper left')\n",
    "    plt.grid()\n",
    "    \n",
    "    plt.tight_layout()\n",
    "\n",
    "plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above includes the wine datapoints on all three different scales: the input scale where the alcohol content was measured in volume-percent (green), the standardized features (red), and the normalized features (blue).\n",
    "In the following plot, we will zoom in into the three different axis-scales."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JH55kXdY69pTs4bUfX+Prgyf2j7fZbZTXlWOxdr1/vK+1jwcYMWIEBoOhZTsyMhKjUV5w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IKFmsYanx0jbCguluSvi9hYWc2t+B1fGKmjga3Al0iT2SsAXQHoR8wWyw4lfQ9UHWB7yXYykzOx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c+6qrxeWRldWmQBQUSHRgbxLcbtgg/fS33eVqs4DpunlrNE3SRe3dKxar2lpRLB55pPemTrtd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\nmZmZmZmZmTXQ/wNPz9EM0qZMXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108fd8828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3, figsize=(6,14))\n",
    "\n",
    "for a,d,l in zip(range(len(ax)), \n",
    "               (df[['Alcohol', 'Malic acid']].values, df_std, df_minmax),\n",
    "               ('Input scale', \n",
    "                'Standardized [$N  (\\mu=0, \\; \\sigma=1)$]', \n",
    "                'min-max scaled [min=0, max=1]')\n",
    "                ):\n",
    "    for i,c in zip(range(1,4), ('red', 'blue', 'green')):\n",
    "        ax[a].scatter(d[df['Class label'].values == i, 0], \n",
    "                  d[df['Class label'].values == i, 1],\n",
    "                  alpha=0.5,\n",
    "                  color=c,\n",
    "                  label='Class %s' %i\n",
    "                  )\n",
    "    ax[a].set_title(l)\n",
    "    ax[a].set_xlabel('Alcohol')\n",
    "    ax[a].set_ylabel('Malic Acid')\n",
    "    ax[a].legend(loc='upper left')\n",
    "    ax[a].grid()\n",
    "    \n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bottom-up approaches"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we can also code the equations for standardization and 0-1 Min-Max scaling \"manually\". However, the scikit-learn methods are still useful if you are working with test and training data sets and want to scale them equally.\n",
    "\n",
    "E.g., \n",
    "<pre>\n",
    "std_scale = preprocessing.StandardScaler().fit(X_train)\n",
    "X_train = std_scale.transform(X_train)\n",
    "X_test = std_scale.transform(X_test)\n",
    "</pre>\n",
    "\n",
    "Below, we will perform the calculations using \"pure\" Python code, and an more convenient NumPy solution, which is especially useful if we attempt to transform a whole matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to recall the equations that we are using:\n",
    "\n",
    "Standardization: \\begin{equation} z = \\frac{x - \\mu}{\\sigma} \\end{equation} \n",
    "\n",
    "with mean:  \n",
    "\n",
    "\\begin{equation}\\mu = \\frac{1}{N} \\sum_{i=1}^N (x_i)\\end{equation}\n",
    "\n",
    "and standard deviation:  \n",
    "\n",
    "\\begin{equation}\\sigma = \\sqrt{\\frac{1}{N} \\sum_{i=1}^N (x_i - \\mu)^2}\\end{equation}\n",
    "\n",
    "\n",
    "Min-Max scaling: \\begin{equation} X_{norm} = \\frac{X - X_{min}}{X_{max}-X_{min}} \\end{equation}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Standardization\n",
    "\n",
    "x = [1,4,5,6,6,2,3]\n",
    "mean = sum(x)/len(x)\n",
    "std_dev = (1/len(x) * sum([ (x_i - mean)**2 for x_i in x]))**0.5\n",
    "\n",
    "z_scores = [(x_i - mean)/std_dev for x_i in x]\n",
    "\n",
    "# Min-Max scaling\n",
    "\n",
    "minmax = [(x_i - min(x)) / (max(x) - min(x)) for x_i in x]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Standardization\n",
    "\n",
    "x_np = np.asarray(x)\n",
    "z_scores_np = (x_np - x_np.mean()) / x_np.std()\n",
    "\n",
    "# Min-Max scaling\n",
    "\n",
    "np_minmax = (x_np - x_np.min()) / (x_np.max() - x_np.min())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to make sure that our code works correctly, let us plot the results via matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qMbAf/pP8Vr0Zai0k3Z5xWGrPqEb0b+BPX14HHA8sakCuUlnq37YAvoMfsCwE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10703a190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2, figsize=(10,5))\n",
    "\n",
    "y_pos = [0 for i in range(len(x))]\n",
    "\n",
    "ax1.scatter(z_scores, y_pos, color='g')\n",
    "ax1.set_title('Python standardization', color='g')\n",
    "\n",
    "ax2.scatter(minmax, y_pos, color='g')\n",
    "ax2.set_title('Python Min-Max scaling', color='g')\n",
    "\n",
    "ax3.scatter(z_scores_np, y_pos, color='b')\n",
    "ax3.set_title('Python NumPy standardization', color='b')\n",
    "\n",
    "ax4.scatter(np_minmax, y_pos, color='b')\n",
    "ax4.set_title('Python NumPy Min-Max scaling', color='b')\n",
    "    \n",
    "plt.tight_layout()\n",
    "\n",
    "for ax in (ax1, ax2, ax3, ax4):\n",
    "    ax.get_yaxis().set_visible(False)\n",
    "    ax.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The effect of standardization on PCA in a pattern classification task"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Earlier, I mentioned the Principal Component Analysis (PCA) as an example where standardization is crucial, since it is \"analyzing\" the variances of the different features.  \n",
    "Now, let us see how the standardization affects PCA and a following supervised classification on the whole wine dataset.\n",
    "\n",
    "\n",
    "In the following section, we will go through the following steps:\n",
    "\n",
    "- Reading in the dataset  \n",
    "- Dividing the dataset into a separate training and test dataset  \n",
    "- Standardization of the features    \n",
    "- Principal Component Analysis (PCA) to reduce the dimensionality   \n",
    "- Training a naive Bayes classifier  \n",
    "- Evaluating the classification accuracy with and without standardization  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading in the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.io.parsers.read_csv(\n",
    "    'https://raw.githubusercontent.com/rasbt/pattern_classification/master/data/wine_data.csv', \n",
    "    header=None,\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dividing the dataset into a separate training and test dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this step, we will randomly divide the wine dataset into a training dataset and a test dataset where the training dataset will contain 70% of the samples and the test dataset will contain 30%, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "X_wine = df.values[:,1:]\n",
    "y_wine = df.values[:,0]\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_wine, y_wine,\n",
    "    test_size=0.30, random_state=12345)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Scaling - Standardization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "std_scale = preprocessing.StandardScaler().fit(X_train)\n",
    "X_train_std = std_scale.transform(X_train)\n",
    "X_test_std = std_scale.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimensionality reduction via Principal Component Analysis (PCA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we perform a PCA on the standardized and the non-standardized datasets to transform the dataset onto a 2-dimensional feature subspace.  \n",
    "In a real application, a procedure like cross-validation would be done in order to find out what choice of features would yield a optimal balance between \"preserving information\" and \"overfitting\" for different classifiers. However, we will omit this step since we don't want to train a perfect classifier here, but merely compare the effects of standardization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# on non-standardized data\n",
    "pca = PCA(n_components=2).fit(X_train)\n",
    "X_train = pca.transform(X_train)\n",
    "X_test = pca.transform(X_test)\n",
    "\n",
    "\n",
    "# om standardized data\n",
    "pca_std = PCA(n_components=2).fit(X_train_std)\n",
    "X_train_std = pca_std.transform(X_train_std)\n",
    "X_test_std = pca_std.transform(X_test_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us quickly visualize how our new feature subspace looks like (note that class labels are not considered in a PCA - in contrast to a Linear Discriminant Analysis - but I will add them in the plot for clarity)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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H2nyuSHXaNHjwYAwePBh+fn7w9fWFnZ2dWiqEtvrZuXMnzp07B2dnZyxZsgST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\nMLOPsXsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3ea2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10,4))\n",
    "\n",
    "\n",
    "for l,c,m in zip(range(1,4), ('blue', 'red', 'green'), ('^', 's', 'o')):\n",
    "    ax1.scatter(X_train[y_train==l, 0], X_train[y_train==l, 1],\n",
    "        color=c, \n",
    "        label='class %s' %l, \n",
    "        alpha=0.5,\n",
    "        marker=m\n",
    "        )\n",
    "\n",
    "for l,c,m in zip(range(1,4), ('blue', 'red', 'green'), ('^', 's', 'o')):\n",
    "    ax2.scatter(X_train_std[y_train==l, 0], X_train_std[y_train==l, 1],\n",
    "        color=c, \n",
    "        label='class %s' %l, \n",
    "        alpha=0.5,\n",
    "        marker=m\n",
    "        )\n",
    "\n",
    "ax1.set_title('Transformed NON-standardized training dataset after PCA')    \n",
    "ax2.set_title('Transformed standardized training dataset after PCA')    \n",
    "    \n",
    "for ax in (ax1, ax2):\n",
    "\n",
    "    ax.set_xlabel('1st principal component')\n",
    "    ax.set_ylabel('2nd principal component')\n",
    "    ax.legend(loc='upper right')\n",
    "    ax.grid()\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training a naive Bayes classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use a naive Bayes classifier for the classification task. If you are not familiar with it, the term \"naive\" comes from the assumption that all features are \"independent\".  \n",
    "All in all, it is a simple but robust classifier based on Bayes' rule\n",
    "\n",
    "Bayes' Rule:\n",
    "\n",
    "\n",
    "\\begin{equation} P(\\omega_j|x) = \\frac{p(x|\\omega_j) * P(\\omega_j)}{p(x)} \\end{equation}\n",
    "\n",
    "where \n",
    "\n",
    "- &omega;:  class label  \n",
    "- *P(&omega;|x)*: the posterior probability\n",
    "- *p(x|&omega;)*: prior probability (or likelihood)\n",
    "\n",
    "and the **decsion rule:**\n",
    "\n",
    "Decide $ \\omega_1 $ if $ P(\\omega_1|x) > P(\\omega_2|x) $ else decide $ \\omega_2 $.\n",
    "<br>\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\Rightarrow \\frac{p(x|\\omega_1) * P(\\omega_1)}{p(x)} > \\frac{p(x|\\omega_2) * P(\\omega_2)}{p(x)}\n",
    "\\end{equation} \n",
    "\n",
    "\n",
    "I don't want to get into more detail about Bayes' rule in this article, but if you are interested in a more detailed collection of examples, please have a look at the [Statistical Patter Classification](https://github.com/rasbt/pattern_classification#statistical-pattern-recognition-examples) in my pattern classification repository.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "# on non-standardized data\n",
    "gnb = GaussianNB()\n",
    "fit = gnb.fit(X_train, y_train)\n",
    "\n",
    "# on standardized data\n",
    "gnb_std = GaussianNB()\n",
    "fit_std = gnb_std.fit(X_train_std, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the classification accuracy with and without standardization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Prediction accuracy for the training dataset\n",
      "81.45%\n",
      "\n",
      "Prediction accuracy for the test dataset\n",
      "64.81%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "pred_train = gnb.predict(X_train)\n",
    "\n",
    "print('\\nPrediction accuracy for the training dataset')\n",
    "print('{:.2%}'.format(metrics.accuracy_score(y_train, pred_train)))\n",
    "\n",
    "pred_test = gnb.predict(X_test)\n",
    "\n",
    "print('\\nPrediction accuracy for the test dataset')\n",
    "print('{:.2%}\\n'.format(metrics.accuracy_score(y_test, pred_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Prediction accuracy for the training dataset\n",
      "96.77%\n",
      "\n",
      "Prediction accuracy for the test dataset\n",
      "98.15%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pred_train_std = gnb_std.predict(X_train_std)\n",
    "\n",
    "print('\\nPrediction accuracy for the training dataset')\n",
    "print('{:.2%}'.format(metrics.accuracy_score(y_train, pred_train_std)))\n",
    "\n",
    "pred_test_std = gnb_std.predict(X_test_std)\n",
    "\n",
    "print('\\nPrediction accuracy for the test dataset')\n",
    "print('{:.2%}\\n'.format(metrics.accuracy_score(y_test, pred_test_std)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the standardization prior to the PCA definitely led to an decrease in the empirical error rate on classifying samples from test dataset."
   ]
  }
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